1966, No. 12

Semiconductor detectors for ionizing radiationW. K. Hofker

539.1.074.55

Following the discovery of semiconductor devices that could perform the circuit functions ofthermionic valves and photoelectric cells - the transistors and photoresistors now so wide-ly used - there has been considerable success in the last few years in the development ofsemiconductor devices which can be used for the detection of ionizing radiation. These detec-tors have some exceptionally valuable features, and it can already be said that their intro-duetion has very considerably advanced the technique of radiation measurement. By wayofintroduetion to future articles, in which the applications of semiconductor detectors will bediscussed, the article below deals with the operation and distinctive features of these newdevices.

Principles and characteristic features of semiconductordetectors

In the last six years or so, great changes have beentaking place in the instrumentation used for detectionand energy-measurement of charged particles, and asimilar situation has recently arisen in y-ray spectre-metry. The conventional instalments for energy meas-urement, such as ionization chambers, proportionalcounters and, to a lesser extent, scintillation counters,are being superseded by detectors of an entirely differ-ent type, i.e. semiconductor counters. These solid-statedetectors (fig. 1) combine small size and ready inter-pretation of the output signals with exceptionally highresolution of the energy of the detected particles orquanta. This high resolution is particularly useful inmany branches of research in nuclear physics. The useof semiconductor detectors has for example made pos-sible experimental analysis of certain disintegrationprocesses whose details could previously only be assum-ed on theoretical grounds. Really accurate measurementof particle or quantum energy is also often importantin certain investigations directed more towards practi-cal purposes, such as process measurements using radio-active indicators, analyses by means of chemical acti-vation, and reactor investigations.

In principle a semicond uctor detector can be regardedas an ionization chamber in which the sensitive vol-ume is a solid instead of a gas: it consists basically of asemiconductor wafer with an electrode on each side.An incident particle or quantum produces a certainionization charge in the semiconductor, just as itwould in a gas, and this gives a pulse of current in an

Jr. W. K. Hofleer is with Philips Research Laboratories, Amster-dam division.

Fig. I. Two types of experimental semiconductor detectors.As their outward form is mainly determined by their mounts(outside diameter about 3 cm), the visible differences are slight.The window has a surface area of 2 to 3 cm''. The lower photo-graph shows an a-particle counter.

external circuit. This in turn causes a voltage pulse toappear across a resistance included in the circuit (fig. 2).The great attraction of using a solid as the detectionmedium is its very much higher absorption, which en-

323

324 PHILlPS TECHNICAL REVIEW VOLUME 27

ables even fast ~-particles to be stopped in a relativelythin layer, making it possible to measure their energywith an instrument of small dimensions. An incidentalbut extremely important advantage is that a semicon-ductor counter can be very much faster than a gas-filled ionization chamber. Of course, the solid used asthe detection medium has to be a material in which theionization-charge carriers - electrons and holes -can move freely under the influence of an electric field

Fig. 2. Diagram and circuit of a semiconductor detector. The de-tection medium (shaded) is between two electrodes, I and 2, towhich a voltage Vo is applied. An incident radiation quantum orcharged particle frees pairs of charge carriers in the detectionmedium. Under the effect of the electric field the charge carriersmove to the electrodes, giving rise to a voltage across R. The effectof variations in Vo is virtually eliminated by means of capacitivefeedback in the amplifier (via capacitor Cr).

and in which they are not lost prematurely due to thepresence of impurities or other crystal imperfections.

The first indication that a solid can act as an ioniza-tion medi urn was found as long ago as 1913 by Rönt-gen and Joffé [11. They established that an insulatingcrystal becomes slightly conductive when brought intothe vicinity of a radioactive source. With the electricalinstruments available at that time, however, it was notpossible to measure the particles individually.

The first solid-state detector capable of countingparticles individually, and which could be used for meas-uring their energy, was not reported until 1945, byVan Heerden [21. The ionization medium used was asilver chloride crystal which was held at the tempera-ture of liq uid air. The resolution, however, was ratherpoor.

The great advances made in this respect in recentyears bave mainly come about because intensive semi-conductor research has made it possible to prod ucesingle crystals of silicon and germanium which com-bine extreme puritywith a very highdegree ofcrystal per-fection. With such starting materials, and using tech-niques partly derived from diode and transistor manu-facture and partly new, solid-state detectors can nowbe made that meet exacting requirements.

The chief characteristic features

The pulse spectra obtained with a semiconductorcounter are very easily interpreted, because the height

of the pulses is proportional to the energy of the detect-ed particle, while moreover the proportionality factoris the same for all kinds of particles - except very heavyones like fission products.

The pulse rise-time, i.e. the time in which the ioniza-tion charge is produced plus the time it takes to travelto the electrodes, can be very short: in certain circum-stances as short as 10-8 s, and never longer than 10-5 sat the very most. As this time mainly determines thenumber of incident particles which the counter canhandle per second, semiconductor counters show a verygood performance in this respect. The short rise timeis also important in the study of coincident phenomena;the shorter the rise time the more accurate is the timediscrimination. This will reduce the number of situa-tions in which two events taking place in rapid succes-sion are mistakenly regarded as coincident.

The energy resolution, as in all ionization chambers,is determined by 1) the electrical noise from the detectorand amplifier, and 2) the statistical fluctuations in theionization process. Both effects are relatively weakerin those counters in which particles of a particularkind and energy bring about stronger ionization, i.e. in

100005.488MeV

j

8000

6000

4000

2000 5.445MeVI

5.391MeV

~

Fig. 30. The a-spectrum of 241Am recorded with a silicon detec-tor for a-particles. The particle energy E is shown on the hori-zontal axis, and the number of pulses per energy interval of 0.25keV is shown on the vertical axis. The width of the strongestline is about 20 keV at half height. Although the energy separa-tion between the lines is about 45 keV (less than I % ofthe particleenergy) it is easy to discriminate between lines.

1966, No. 12 SEMICONDUCTOR DETECTORS

which the average energy required for producing apair of.charge carriers is lower. Semiconductor counters owetheir exceptionally high resolution principally to thevery small average ionizing energy of silicon and germa-nium (3.6 and 2.9 eV) respectively, compared withabout 30 eV for argon). For the detection ofX-rays andy-rays the resolution of the detector is in fact so goodthat even the best low-noise amplifiers that can nowbe built are barely good enough to do full justice to it.Some semiconductor counters do, however, have to becooled, e.g. to liquid nitrogen temperature (77 OK), tolimit the noise contribution from the bias current.Fig.3 shows a- and y-spectra recorded with semicon-ductor counters, and for comparison a y-spectrum ofthe same radioactive substance, recorded with ascintillation counter.

various branches of nuclear engineering.A feature useful in some types of research is the fact

that semiconductor detectors can be made so thin thatthe particles are able to pass through them with verylittle loss of energy. The detector is then used, of course,not to measure the energy of the particle but the energyloss per unit path-length. This quantity is of interest inestablishing the identity of an unknown particle.The last important advantage to be mentioned is the

very small effect which variations in the supply volt-age have on the output signal when a suitable circuit isemployed; the scintillation counter and the proportio-nal counter, on the other hand, require highly stabilizedpower supplies.

In the following sections of this article we shall dealfirst with the processes takingplace in the detection med-

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Fig. 3b. Part of the ,,-spectrum of 166mRo, recorded with a germanium counter. Each point represents the number of pulses in anenergy interval of 2 keY. A very large number of separate lines can be distinguished; the quantum energy for most of them isindicated separately. The dashed line indicates the spectrum found with a scintillation counter. (For clarity this is shown at about100 times the measured value.)

The design of a semiconductor detector can readi-ly be adapted to the nature and energy of the particlesto be detected and to the purpose for which it is to beused. There are detectors for a-particles, for hard y-radiation, for X-rays, and so on.Another feature is that the single electrodes on each

side of the semiconductor wafer can be replaced by aseries of separate strips. If the strips on one side arealigned perpendicular to those on the other, the detec-tor is divided into a large number of subdetectors, sothat the place where a particle enters can be determin-ed accurately [3j ("checker-board counter",jig. 4). Thisapproach is of interest in nuclear physics and also in

ium. We shall then briefly consider the principal effectsdetermining the resolution and discuss the merits ofvarious counter configurations. Finally, the characteris-tic features of semiconductor counters will be com-pared with those of proportional counters and sein-tillation counters.

[1] W. C. Röntgen and A. Joffé, Ann. Physik 41,449, 1913 and64, 1, 1921. .

[2] P. J. van Heerden, The crystal counter, thesis, Utrecht, 1945.See also P. J. van Heerden, Physica 16, 505, 1950 and P. J.van Heerden and J. M. W. Milatz, Physica 16,517, 1950.

[3] This type of counter was developed in co-operation with ateam of physicists from the Instituut voor Kernfysisch On-derzoek (Institute.for Nuclear Physics Research), Amster-dam.

325

0.8

326 PHILIPS TECHNICAL REVIEW VOLUME 27

The ionization process in a semiconductorWhen a high-energy charged particle or a quantum

of radiation moves through a medium it dissipatesenergy in it. In the process, atoms of the mediummay become ionized. In this section we shall examinemore closely just how this takes place, particularly insemiconductors, and show that in a given substancethe average energy w required for a single ionization isindependent, in the first instance, of the nature of the

low owing to the differences of mass involved - forexample a 6 MeV a-particle can transfer at the mostonly 3 keY to a stationary electron - but even so itis usually more than sufficient to free the electron fromthe atom. This is known as primary ionization. Amuch greater part of the ultimate ionization chargeis due, however, to secondary ionization. This is large-ly brought about by the electrons freed by primaryionization. Some electrons are also freed by the Auger

Fig.4. Semiconductor detector for determining directional distribution ("checker-boardcounter"). This detector has a series of electrodes on opposite sides in the form of strips. Thedirection of the electrodes on one side is perpendicular to that of the electrodes on the otherside (see mirror image; the line crossing this is the lower edge ofthe mirror, twice reflected).

radiation and of the energy of the particles (quanta).A charged heavy particle (proton, a-particle), loses

most of its energy in collisions with electrons, and asmall part in collisions with atomic nuclei. The energytransferred to an electron upon a collision is relatively

effect: when an electron freed from a deeper shell by theprimary radiation is replaced by an electron from aperipheral shell, the released energy is not alwaysemitted in the form of a quantum of radiation but issometimes transferred to another electron, which then

1966, No. 12 SEMICONDUCTOR DETECTORS 327

leaves the atom. If we assume that the primary and sec-ondary ionizations take place one after the other, wecan represent the situation arising after each of the twophases in a semiconductor by an energy band diagramlike that in fig. 5.

Ionization by y-particles or accelerated electronstakes place basically in the same way. Owing to theequality of the masses involved, however, a single colli-sion can result in a much greater part of the energy (upto 100%) being transferred to a stationary electron.

A charged particle travelling at very high speed alsoloses some of its energy through the emission of elec-tromagnetic radiation. The intensity of the radiationis proportional to the square of the atomic number ofthe medium. For electrons in germanium this effectonly becomes ofsignificance when the particle energy isgreater than 10 MeV. For heavy particles it can beentirely disregarded, since it only becomes noticeablein the GeV region.

Because of the relatively high density of solids therange of particle radiation in them is very much smallerthan in gases. For example, the range of I MeV ~-par-tides in silicon is 2 mm, compared with 3.75 m in

v

Fig. 5. a) Immediately after the incidence of a quantum or parti-cle, there are freed charge carriers in the conduction and valencebands (C and V) as well as electrons in higher bands and holes inlower bands.b) A short time later, all electrons are in the lowest levels of theconduction band (lower limit Ee) and the holes are in the highestlevels ofthe valence band (upper limit Ev). In addition large num-bers of secondary electrons and holes have been freed. The dif-ference E« - E; is the energy gap LIE.

air ; the range of 10 MeV a-particles - the highestenergy particles emitted by the nuclides known atpresent - is only about 70 urn in silicon. A thinwafer of the detection medium can therefore beused; for a-detectors this need only be very thin.

The ionization due to y- or X-radiation differs fromthat due to charged particles in that the primary ioni-zation is brought about by three different effects: thephotoelectric effect, the Cornpton effect and pair for-mation .In the photoelectric effect the quantum energyE is imparted entirely to the freed electron. In pairformation an electron and a positron (positively chargedelectron) are created, which together receive the energyE - 1.02 MeV. In the Compton effect a variable partof the quantum energy is transferred to the electron.The probability of the occurrence of these processes isa function of E and of the atomic number Z of theionization medium. The probability of the photoelec-tric effect, for instance, is proportional to Z5£-3.5. Itthus increases sharply with increasing Z and de-creases sharply as E is increased. The probability ofpair formation is proportional to Z2, and increasesslightly with increasing E, initially in proportion to E- 1.02 MeV, but less at greater E_ Because both effectsincrease with increasing Z, the relatively heavy germa-nium (Z = 32) is preferable to silicon (Z = 14) for ay-detector. Gamma radiation penetrates deeper intothe substance than particle radiation of the same energy.For energy measurements on y-quanta of about1 MeV the semiconductor layer must be several mmthick.

Relation between ionization charge and energy

In a fairly wide range of energies the ionizationcharge, within the accuracy ofmeasurement, is propor-tional to the energy of the particles (quanta) and inde-pendent of the nature of the radiation. This inde-pendenee is understandable when we consider thationization is entirely due to electrons for v-quanja and~-particles and very largely due to electrons for heavyparticles.

The average energy w required for a single ionizationis, as we have seen, much lower in solid-state detectorsthan in gases, but it is still considerably greater thanthe energy gap LIE. For germanium HI = 2.9 eV,against LIE = 0.65 eV; in silicon HI = 3.6 eV, againstLI£ = 1.1 eV. There are two reasons for this inequali-ty: 1) part of the energy of the freed electrons is used forlattice vibrations and 2) electrons whose energy hasdecreased to less than LI£ can no longer cause ioniza-tion, so that this residual energy plays no part in theionization process. In any case, then, HI will be greaterthan LIE.

For heavy particles there is in theory some deviationfrom linearity in the relation between E and the ionizationcharge, because these particles can no longer cause ionizationwhen E has dropped to a value which is still well above LIE.For a-particles in silicon this threshold value is about 1 keY.Altho~h this is a large multiple of LIE, it is nevertheless such a

r-----------------------------------------~ '--"~""'-',

328 PHILIPS TECHNICAL REVIEW VOLUME27

small fraction of the normal initial value of E that the deviation we shall be concerned purely with barrier-layer types,is not detectable in the experimental results. If the ionization unless otherwise stated.medium is a gas, this threshold value may be very much higher,and a marked deviation is indeed found for heavy particles of notunduly high energy [4J. A complication may arise from the effect in which clouds of

positive and negative charge carriers, as soon as they are separatedby the electric field, are in principle neutralized by charge car-riers of opposite sign which come from the surroundings and fromthe electrodes. This neutralization varies exponentially with time.The time constant "reI, the dielectric relaxation time, is equal toela, where e is the dielectric constant and a the conductivity ofthe material. The above treatment of the charge collectionapplies, strictly speaking, only for "rel = CO. In detectors inwhich the natural material contains hardly any charge carriers,and where none can come from the contacts, the neutralizationis virtually negligible.

From ionization charge to pulse

We shall now examine what happens when the ap-plied field causes the ionization charge to move towardsthe electrodes. This determines the form of the pulseobserved in the external circuit in the detection of aparticle. We shall assume to begin with that none ofthe ionization charge is lost on the way, that the detec-tion medium has a large energy gap (so that, in the nat-ural state, there are virtually no free charge. carriersin the ~edium), and that no charge carriers can pene-trate into the medium from the electrodes.In every ionization event two charge carriers of oppo-

site sign are produced. When an electric field isapplied (due to a voltage Vo) the freed positive and neg-ative charge carriers (each with a total charge Qi)move away from one another and a charge is inducedin each of the two electrodes 1 and 2 (fig. 2). If the twokinds of charge carrier have become separated by adistance equivalent to a potential drop of LI V, then theinduced charge [5] has a magnitude of QiLl VIVo. Thevoltage across the resistor R (fig. 2) at that moment is .(Qi/C) (L1VIVo), where C is the capacitance of the elec-trode 2 with respect to earth. Now if the time constantRC is large compared with the time in which the ioni-zation charge is collected at the electrodes, then thefinal value of the voltage across R - i.e. the height ofthe voltage pulse - is equal to Qi/C, hence proportio-

• nal to Qi and independent of Voo (If the charge collec-tion time is not short with respect to RC, then the pro-portionality with Qi remains but the final value is lowerthan Qi/C and no longer independent of Vo.)The above picture of a semiconductor detector is, of

course, over-simplified: some charge carriers from theelectrodes will always penetrate into the medium, andeven without this the medium in the natural state con-tains a certain number of free charge carriers.In counters for particle and gamma spectrometry,

which should therefore have a very high energy resolu-tion, these effects must be suppressed as far as possible.In counters, on the other hand, which are only requiredto measure the average intensity of a stream of particles(quanta), such as counters for dosimetry, there may beadvantages in a ready flow of charge carriers from theelectrodes (injection contact), since the sensitivity canbe increased by this [6]. Counters with injection con-tacts are called conduction counters, and the othersare known as barrier-layer counters. In the following

('

Life of charge carriers and pulse height

In the foregoing we have assumed that all chargecarriers freed by the incident radiation do in fact reachthe electrodes. In reality a number ofthem will not, butwill be trapped on the way and may even recombine.Obviously, there will be less probability of their recom-bining if the travelling time of the charge carrier -maximum value equal to the carrier transit time -is short compared with its average life. For a group ofcharge carriers that has to cover the whole distance dbetween the electrodes it has been calculated that afraction [1- {l- exp (-dll17:F)}/J:rFld] are lost. In thisexpression F is the electrical field strength, assumingthe field to be uniform, and fk the mobility ofthe chargecarriers. At a given d and F the product fk7: thereforedetermines the magnitude of the loss. It should be re-membered here that fk7: does not in general have thesame value for holes and electrons. The greatest signalloss is found when the particle to be detected is inci-dent at a place such that the charge carriers with thelowest fk7: value have to travel through the whole crys-tal.

Since the signalloss depends on the place of incidence,pulses produced by particles of identical E do notall have the same height. For a good energy resolution,therefore, the signalloss must be kept relatively small.It follows from the formula just given that we mustmake fk7:F large with respect to d, i.e. dlF small withrespect to fk7:. (If this condition is satisfied, the expres-sion for the relative loss approximates very closely todI2fk7:F.). If we now reduce the condition above to dl fkF «7:

we see at once the relation to the qualitative approachat the beginning: since the velocity of a charge carrieris p.F, dl fkF is the carrier transit time, and therefore,taking a value for fk corresponding to that of the slow-est charge carriers, dl fkF is the maximum value te max ofthe charge collection time. The condition for a relative-ly small signalloss is simply te max « 7:.

1966, NO.'12 SEMICONDUCTOR DETECTORS 329

Pulse rise-time

If we wish the detector to have a very high resolut-, ion in time and if we require it to be able to handle ahigh count-rate without the pulse height being seriouslyaffected by the superposition of pulses, we must ob-viously try to obtain the shortest possible pulses. It iscomparatively easy to reduce the pulse decay time: thiscan be done electronically, e.g. by differentiation. Therise time, however, is entirely determined by one ofthe processes that takes place in the detector itself: thecollection of the charge. The ionization process usuallytakes place much faster.We have seen that the collection time is at the

most dffhF (or d2ffhVo). Depending on the design ofthe detector, values are found between 10-5 and 10-s.On the other hand, the duration of the primary ioni-zation process - i.e. the time that elapses between theentry of the particle and the moment at which it causesno further ionization - is only about 2.5X 10-12 s fora 5 MeV a-particle in silicon, and the duration of thesecondary ionization process, which may be similarlydefined, is of the same order of magnitude.To obtain a short rise time it is thereforenecessary to

impose on the maximum charge collection time te max

a condition similar to that laid down for obtaining asmall signal loss, the difference here being that theabsolute value of te max must be small. This is the caseif d is small and if fh and Vo are large. The requirementfor large Vo indicates that the,breakdown voltage of thecounter should be as high as possible.

In the above we have tacitly assumed that the ionization chargesare not dense enough to seriously affect the field in the detec-tion medium by polarization. With heavy particles, however,which produce a very dense charge cloud, polarization may in-deed occur (jig. 6). Inside the cloud the field strength F is theninitially very small, and does not assume an appreciable value un-til the cloud .has thinned out due to ambipolar diffusion of thecharge carriers - at right angles to the direction of the field -and the loss of peripheral charge carriers.It is evident that in such a case the collection of the ionization

charge will not be so fast. For a 5 MeV a-particle, incident per-pendicular to the field direction, and a field strength of 1000 V[ctt:we have calculated that the collection time (e can be lengthenedat the most by 0.3 !Ls.Usually, however, this time is much less,so that the effect IS not particularly serious.It should not be concluded from the above that the recornbina-

tion charge loss associated with the delay is of no significance.In a dense charge cloud - a region therefore where the coneen-trations of both kinds of charge carrier are very high - the pro-bability of recombination is much greater, and hence 1: is muchsmaller than in a rarefied cloud. The recombination loss for heavyparticles is therefore already greater than for light ones, so thata longer collection time is more serious here. Since the magnitudeofthe recombination loss will differ from case to case, the polari-zation effect adversely affects the resolution. This is one of thereasons why the resolution for a-particles is not as good as forp-particle(of the same energy.

+-

Ft-----'

f

Fig. 6. If the charge-cloud is extremely dense, as it is with veryheavy particles, polarization occurs as soon as the negative andpositive charge carriers move apart. The field strength F is thenpractically zero inside the cloud; see the field variation shownbelow.

Energy resolution

In the preceding section we have already indicatedthat the resolution is limited when the collectedcharge, and hence also the height of the output pulse,depends to some extent on the place where the particleis incident. In this section we shall consider two othercauses of fluctuations in the pulse-heights, namelyphenomena which occur in the detector itself andmoreover directly depend on the configuration ofthe detector (dimensions, nature of contacts) as wellas on the nature of the detector material [7l. Theseare: 1)fluctuations in the ionization charge, and 2) flue-tuations in the bias current through the detector, the"dark current".The fluctuations in the ionization charge come about

because only a part of the energy of an incident particleis used for ionization processes, the rest of the energybeing used to set up excitations such as lattice vibra-tions. Since excitations are probability processes, theionization charge produced by particles of identicalenergy will show statistical fluctuations. If the averageionization charge of a number of mono-energetic parti-

[4] See the article by H. W. Fulbright in Hb. Physik XLV(Springer, Berlin 1958; ed. S. Flügge), in particular fig. 5 onpage 12.

[5] For the mathematical treatment, see D. H. Wilkinson, Ioni-zation chambers and counters, Cambridge Univ. Press 1950.

[6] See L. Heijne, Physical principles of photoconductivity, Ph i-lips tech. Rev. 25, 120-131, 1963/64, in particular page 129.

[7] For a treatment of noise in a detector-amplifier combination,see: J. A. W. van der Does de Bye, Signal-to-noise ratio of aP-N-junction radiation counter, Philips Res. Repts. 16, 85-95,1961.

r--"""~~~~---------------------------~--- .-

330 PHILlPS TECHNICAL REVIEW VOLUME27

cles is expressed by the number of pairs of freed charge.carriers No, then the standard deviation oNo in thisnumber is equal to VF*No. The relative standard de-viation is thus given by:

fJNo = 'VF* = 1/F*w .No No E

In these expressions F* is a constant, called the Fanofactor [81, which depends on the material and on thetype of radiation; wand E are again the average ioni-zation energy and the energy of the incident- particle,so that No = Ejw. One of the advantages mentioned inthe introduetion for the semiconductor detector canreadily be derived from eq. (1): there is a relativelysmall spread in No because the average ionization ener-gy is low. Moreover, measurements have shown [91

that the Fano factor for semiconductors is also rela-tively' small (F = 0.1 to 0.15 compared with 0.2 to0.3 for gas ionization chambers). Using eq. (1) to cal-culate the relative standard deviation in the ionizationcharge of particles of 5 MeV in silicon, we find 3X 10-4,which corresponds to 1.5 keY. Calculating from thisthe half-height width of the pulse-height distribution- this width is 2.36 times as large as fJNo/No and isoften used as a measure of the resolution - we find3.5 keY..As in other semiconductor devices, in nuclear radia-

tion detectors the bias current is a factor that calls forcareful attention with regard to noise. The noise in thebias current has almost entirely the character of shotnoise. This is obvious for the part of the bias currentoriginating from the contacts. In the part due to thermalgeneration of charge carriers in the detector material,the generated charge carriers disappear very quicklyfrom the detector volume because of the effect of theelectric field, so that scarcely any recombination takesplace, the transist time being short compared with theaverage life of the carriers. There is consequently no

. generation-recombination noise, but only a noise con-tribution from the generation process separately. Thisnoise however also has the character of shot noise.

Another point to be noted about the current noise isthat noise-smoothing due to space charge - as inthermionic valves - hardly occurs at all because theconcentration of charge carriers is too low.

These considerations indicate that in calculating theoutput signal fluctuations which result from the bias-current noise we may start with the relationship [101:

i2 = 2eIdf.

Here i is the effective value of the shot noise in the biascurrent in the frequency band dj, e is the absolute chargeof the electron and I the bias current in the detector.It is found that these fluctuations are relatively small

(1)

when VN, the square root of the number of free chargecarriers in the counter, is small compared with the ioni-zation charge No. What this means in practice can bestbe seen from an example. An a- or ,B-particleof 5 MeVproduces 1.5 X 106 pairs of charge carriers in silicon.If we now require a signal-to-noise ratio of at leastlooo : 1, then N must not be greater than 5X 106. Nowin extremely pure silicon at room temperature the con-centration of charge carriers is already between 1011and 1012 cm-3• In a counter of not excessively smalldimensions this means that N would be much toogreat if no special measures were taken to reduce it.In the following section we shall consider what meas-ures can be taken.

(2)

Detector configuration

Semiconductor detectors can be divided into twobasic groups with different electrical configurations:detectors with injection contacts - conduction count-ers - and detectors with blocking contacts - barrier-layer counters. This classification has already brieflybeen mentioned. The nature of the contacts affectsnearly all the questions relating to the type and opera-tion of the detectors, one of the most important beingthe manner in which the number of free charge carriers.N is reduced to improve the signal-to-noise ratio. Weshall therefore begin with a brief account of both kindsof detector, commenting brieflyon the requirementsto be met in both cases by the semiconducting material.We shall then leave the subject of conduction coun-

ters, which have been very little used up till now, anddevote the rest of this section to the different typesof barrierlayer counter, and to the question of whichtype is most suitable for a given form of radiation.Since conduction counters have injection contacts,

the concentrations 11 and p of the free electrons andholes do not depend on whether or not an electricfield is present: charge carriers leaving the detectionmedium under the effect of such a field are immediatelyreplaced by others entering through the other contact.The values of 11 and p, and hence N itself, cannot there-fore be affected by means of the field. In these detectorsthe bias current depends entirely on the nature of thedetector material and not at all on the contacts.In barrier-layer counters, on the other hand, N is

certainly affected by the applied voltage, because chargecarriers drawn away from the medium are only replacedto a very limited extent. Where signal-to-noise ratio isconcerned a barrier-layer counter is therefore in prin-ciple preferable to a conduction counter made of thesame material.. In order for the field in a counter of any kind to bereasonably uniform, the space charge should be nearlyequal to zero everywhere inside it. In conduction coun-

1966, No. 12.

SEMICONDUCTOR DETECTORS 331

ters this happens automatically because free chargecarriers can flow unimpeded to neutralize boundcharges. In barrier-layer counters, however, the spacecharge is zero only when the detection medium con-tains no bound charges, that is to say when it is anintrinsic semiconductor, or when the positive andnegative bound charges are equal and thus neutralizeeach other. (In the last case, also, a semiconductor isoften said to be "intrinsic", because the holes and elec-trons have the same concentration, so that the Fermilevel also lies half-way up the energy gap.)The materials suitable for use as the detection med-

ium are at present few in number: for barrier-layercounters the choice is practically limited to germa-nium and silicon. The usefulness of these two sub-stances is due to the following circumstances:1) The charge carriers have a long life (0.1 to 1 ms)

and at the same time a high mobility. The productf1:r: is therefore so large that, without any great loss,the ionization charge can be collected in a layer asthin as 1 cm. In other semiconductors the carrierlife is generally much shorter (10-7 to 10-8 s).

2) Considerable advances have been made in the pro-duction of large single crystals of well defined andreadily processed germanium and silicon.

For conduction counters, however, silicon and germa-nium are unfortunately not so suitable, for reasonsthat will presently appear. First of all, we shall considerthe conduction counter in somewhat more detail, andthen we shall confine our attention to the barrier-layercounters.

Conduction counters

In a conduction counter the concentrations nand pof the negative and positive charge carriers respectivelyare equal to those present in the medium in the absenceof an applied voltage. The well-known equation.

n p oc exp (-!JE/kT).

then applies. The product np is usually represented by/1f2. If bound charges are present, nand p must alsomeet the neutrality condition:

11 + Na = p + N«.

Here Na and Nd are respectively the concentrations ofthe singly charged negative and positive. impuritycentres.It follows from eq. (3) that the sum 11 + p is smallest

if 11 = p, i.e. if Na = Nd. Quantitatively, at room tem-perature 11 + p is smaller than 106 cm-3 -, for acounter of 1 cmê, i.e. a counter in which N = n +p,this corresponds approximately to the requirement fora signal-to-noise ratio of 1000 : 1- only if the energygap is larger than 1.65 eV and the difference between

(3)

Na and Ne is smaller than 106• Materials which satisfythis condition, and in which the charge carriers havesufficiently long life, are not yet available. For thepresent the only choice is to make do with materials ofsmaller energy gap, but this implies that cooling mustbe applied in order to reduce 11i2• In the hypotheticalcase in which Na-Nd = 0, Si would have to be cooledto -75°C, and Ge to -140°C,

Even the purest germanium and silicon monocrystalsthat can be made at present do not at this temperaturesatisfy the condition that Na - N« should be less than106 in a not too small volume. Further measures there-fore have to be taken, such as:1) reducing the temperature much further than would

be necessary in the intrinsic case. A greater numberofimpurity centres will then change to the unchargedstate. The extent to which it is necessary to cool thematerial in order to achieve a significant reductionof Na and Nd depends, of course, on the location ofthe impurity levels. In silicon, for example, theboron atoms present as impurities giverise to impur-ity levels that are only 0.045 eV above the conduc-tion band, and this necessitates cooling to between10° and 20 oK.

2) reducing the difference between Na and N« means ofappropriate doping. Use can then best be made ofsubstances that have impurity centres lying approxi-mately at the centre of the forbidden band, i.e. atthe height where the Fermi level should be.The quan-tity of dope used is then less critical. A diffi-culty with this method is that impurity levels of thiskind constitute effective recombination centres, andthus shorten the life of the carriers.Earlier in this section it was stated that intrinsicmate-

rial (type I) should be used for a barrier-layer counter toobtain uniformity of the field. It is clear from theabove that the same requirement holds in principle forconduction counters, but now for the purpose of ob-taining a minimum noise level.

(4)

A familiar example of the method mentioned under 2) is thedoping of N-type silicon with gold, producing electron trapswhich are located 0.54 eV below the 'conduction band (LlE =1.1 eV). If the gold concentration has three times the value thatNd previously had, then 11 "" P in a wide temperature range [111.

Counters that work reasonably well have been made with amaterialof this kind [121.

[8] U. Fano, Phys. Rev. 72, 26, 1947.[D] R. L. Heath, W. W. Black and J. E. Cline, IEEE Trans. nuel.

Sci. NS-13, No. 3, 445, 1966.[10] See A. van der Ziel, Fluctuation phenomena in semi-conduc-

tors, Butterworths, London 1959. .[11] C. B. Collins, R. O. Carlson and C. J. Gallagher, Phys. Rev.

105, 1168, 1957.[12] J. D'. van Putten and J. C. Vander Velde, IRE Trans. nucl.

Sci. NS-8, No. 1, 124, 1961.

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332 PHILIPS TECHNICAL REVIEW VOLUME27

Barrier-layer counters

In barrier-layer counters the charge carrier concen-tration is mainly determined by the contacts and theapplied voltage, and to a much lesser extent by thenature of the material. The requirement that intrinsicmaterial should preferably be used is not in the firstplace due to noise considerations. The significanee ofthe energy gap will be discussed presently.An important question here is how to obtain contacts

that have an adequate blocking action. As a rule, thiscan be achieved by doping. In our counters the anodeis generally a semiconducting surface layer of stronglyN-type material, and the cathode a thin layer of strong-ly P-type material. In the latter material there are veryfew electrons in the conduction band, and thereforethe P contact cannot supply a large number of elec-trons in a short time. The same applies to the N con-tact with respect to the holes. Fig. 7 shows the band dia-gram of a P-I-N system of this type when a voltagehas been applied to it. .. To get some idea of the charge-carrier concentrationin the I-region when a voltage has been applied to thecounter, one must first realize that the free charges inthis region partly originate from the electrodes andpartly from thermal generation. In practice sufficientlygood blocking contacts can be obtained to make thecontribution from the electrodes negligible, leavingonly the thermal generation to be reckoned with. Theelectron carrier concentration resulting from this de-pends on the speed at which the freed charge carriersleave the detection medium under the effect of theelectric field.In our case thermal generation via an impurity level

predominates - i.e. generation in two steps. If the im-purity levels lie at the centre of the forbidden zone -the most unfavourable case - the number of pairs ofcharge carriers generated per cm3 is nl/2-c, where -cis again the life of the carriers. The number of pairs Ggenerated in the whole counter volume is thus niAd/2-c,where A is the surface area. On the other hand, theaverage time that an electron remains in the detectoris equal to d/2p,nF. Fór a hole this time is d/2p,pF. Thenumber of charge carriers is now equal to G times thisaverage time, so that, with F again put,equal to Void,wefind for the sum of the number of holes and electrons:

d3An1(I 1)N = 4Vo-c p,n + ftp •

Applying this to a silicon counter (m = 1010 cm-3and -c= 10-3 s) with a thickness dof 5 mm, a surfacearea A of 1 cm'' and an applied voltage Vo of 500 V,we find N = 1.7X 106,which is an acceptable value. Ingermanium, because of the smaller energy gap, n, is

. . . (5)

p+ I

o d_X

Fig.7. Simplified energy-band diagram (potential variation inthe x-direction) for a counter with P-I-N configuration with anexternal voltage Voo (In reality e Vo is very much greater thanEc - Ev.) The chain-dotted line in the contacts indicates the lo-cation of the Fermi level EF. If the I region is completely free ofimpurities, Ec and E« vary almost linearly with x in this region.

higher (1013 cm-3) and in the conditions mentioned Nis higher than desirable. To make N sufficiently lowthe material therefore has to be cooled.We shall now consider the situation when the de-

tector material is not intrinsic but to a certain extentP-type or N-type. Fig. 8 illustrates the case where thedetection medium is weakly P-type. The counter con-figuration has now in fact degenerated to a P-N junc-tion. The volume within which the field is reasonablystrong and in which the ionization charge can thus becollected (the effective volume) is reduced to the barrierlayer. Although charge carriers freed outside the barrierlayer have a chance to diffuse towards the barrierlayer and make their contribution there, this contribu-tion is rather small, for one reason because of the rela-tive slowness of a diffusion process.It should not be concluded from the above that the

sensitive layer of counters with a P-N structure is nec-essarily extremely thin. From the equation for thewidth B of a depletion layer

B = V2e(Vd + Vo), . . . . (6)eNa

a depletion layer width ofO.5 mm is found for extreme-ly pure silicon with a concentration Na of 1012 cm-3,at an applied voltage of 200 V. (Equation (6) is appli-

1966, No. 12 SEMICONDUCTOR DETECTORS 333

p+ p

o _x d

Fig. 8. As in fig.7, but now for the case where the detectionmedium is not intrinsic but to a certain extent P-type. The con-figuration has virtually degenerated into a P-N junction, andthe detection medium has a sufficiently strong field only in thelayer immediately bordering on the N-contact.

cable if the concentration of impurity centres in theN-region is much greater than that in the P-region. Thediffusion voltage Vd is negligible compared with 200V.)The last configuration to the mentioned is the one in

which the depletion layer of a metal-semiconductorcontact is used instead of the depletion layer of a P-Njunction. The metal generally used is gold.

Method ofmaking a P-I-N configuration

To make a P-I-N configuration [131 we start from asingle-crystal wafer of fairly pure P-type germaniumor silicon (resistivity about 500Q cm). Lithium isthermally diffused at a few hundred degrees eentigradeto a depth of about 0.2 mm on one side of thematerial. Lithium acts in this as a donor. At the surface,where the lithium concentration is high, the materialthus changes into an N-type semiconductor (fig. 9a).Since the lithium ions occupy interstitial sites in the

lattice, they are to some extent mobile. When a reversevoltage is applied to the resultant P-N junction, at atemperature of say 125 DC, the lithium ions in the re-gion around the P-N junction, where the field strengthis relatively high, begin to move towards the P-region.After a certain time the situation shown in fig. 9b isobtained: a large I region has been produced. The

[13] This method is due to E. M. Pell, J. appI. Phys, 31, 291,1960.

reason for this is briefly as follows. As long 'as theacceptors present are not exactly compensated by li-thium, the field in the material is not homogeneous, andthe lithium ion current varies from place to place inthe crystal in such a way that the differences in con-centration are levelled out.

This attractive method is unfortunately not applicable forthe preparation of I material for conduction counters: afterobtaining the P-I-N configuration the Pand N layers cannotbe removed. These layers are not only necessary for the produc- ,tion of the [layer; they are also required for its maintenance,at least when there is an electric field.

Some practical examples of barrier layer counters

Fig. la shows a diagrammatic representation of asemiconductor detector for a-particles. The materialused is silicon. Since the range of a-particles is relativelyshort, a P-N junction or a blocking metal-semicon-ductor contact with a depletion layer width of 0.1 to0.2 mm is sufficient in a-counters. The particles are in-cident through one of the electrodes, which must bevery thin in order to minimize energy losses. The spec-

\\

10'7

10'4 \\\

10'3

1O'2f.-, --+-L--_I II :_yI II I

,IIII I

'N'-y

i [N P

gP

Fig. 9. Illustrating how, starting with a wafer of P-type material,a P-I-N configuration is obtained by addition of lithium, whichfunctions as a donor in silicon and germanium.a) Variation of the lithium concentration Nd with the distance yto the surface, after the lithium has been thermally diffused intothe crystal wafer. The concentration No. of the acceptors is in-dependent of y. In a thin layer at the surface, N« is greater than No.and the material has changed from P-type to N-type. (The verti-cal scale is only very approximate.)b) Variation, of N« with y after some ofthe lithium ions have pen-etrated deeper into the wafer under the effect of an electricfield and at elevated temperature. In a wide region around theP-N junction in (a) Nd has become equal to No. and the material'is therefore intrinsic. If the lithium supply is adequate the extentof this region increases with the time the process lasts.

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334 PHILIPS TECHNICAL REVIEW VOLUME27

IX IX

l l- N+

Bl_ __: .__ ~ PR

Fig. 10. Configuration of an a-detector, consisting of a PoN junc-tion with a relatively wide barrier layer (width B).

trum shown in fig. 3a was recorded with a counter ofthis type. A photograph of the counter can be seen inthe lower photograph of fig. 1.Because of the much greater range of high-energy

,B-particles,a P- N junction is not adequate for measuringtheir energy, and in this case a counter of P-/-N struc-ture with an I layer a few millimetres thick (fig. 11)should be used.Counters with P-I-N structure are also needed for

the detection of y-radiation. In this case, as mentionedabove, germanium is to be strongly preferred becauseof its higher atomic number. The spectum shown infig. 3b was recorded with a germanium P-/-N detector.As y-quanta can penetrate a relatively long way into

light materials without any interaction taking place,y-counters can be completely encapsulated and thusprotected from atmospheric effects.As mentioned in the introduction, extremely thin

semiconductor detectors are employed in particle-identification systems. In systems of this kind separatedetectors are used for measuring the energy E of aparticle and the energy loss per unit path length, dE/dx.For identifying the nature ofthe particle, use is made ofthe fact that the product EdE/dx isproportional to mZ2

and largely independent of E (fig. 12). For protons,deuterons, tritons and a-particles, for example, the ra-tios of these products are 1 : 2 : 3 : 16.The energy lossper unit path length is measured with the thin semi-conductor detector mentioned above, in which theparticle loses relatively little energy (upper photographfig. 1). In fact, of course, dE/dx is not measured, but(jE/d, where (JE is the energy loss. When the particlehas passed through this ~etector it is stopped in theother, enabling E to be measured.The thickness of the dE/dx detector is chosen be-

tween 25 to 250 (Lm depending on the natureof the experiment. A poN detector with a highenough applied voltage to make the depletion layer ex-tend to the other side of the layer forms a particularlysuitable dE/dx detector. For E measurements a siliconP-I-N detector is generally employed.

Apart from the electrical structure of the detector

Fig. 11. In detectors for energy measurement on y-quanta or long-range particles (high-energy {J-particles) a PoN junction is notsufficient; such detectors should have a P-/-N configuration.

-- poN or P-/-N -- the geometrical structure can alsobe varied in many ways. We have already mentionedthe "checker-board counter", which can be used toperform very accurate directional measurements in a'short time (fig. 4). With these detectors, which aredivided into some 40 subdetectors per cm", a resolu-tion of about 10 can be achieved in a directional meas-urement with a distance of only 8 cm between sourceand detector. It is also possible to design dE/dx detec-tors as checker-board counters if required [14]. There

104,---------------------------,

n

v10~~ __~L------+_----~L-I~

1 2 3_mZ2

Fig. 12. Spectrum of IIIZ2 values (Ill = nuclear mass and Z =atomic number) obtained in measurements made with a particle-identification system on a beam containing protons, deuteronsand tritons; we have taken mZ2 = I for the proton. The valueof mZ2 is calculated for each incident particle from the productof the particle energy E and the energy loss per unit path lengthdEldx. These two quantities are measured with separate detectors.

1966, No. 12 SEMICONDUCTOR DETECTORS 335

are other detectors in which a beam of particles ispassed through a central hole; this arrangement canbe used to detect particles scattered backwards from atarget situated some distance further on.

Comparison with proportional counters and scintillationcounters

Linearity and energy resolution

We have seen that the pulse height in semiconductorcounters is proportional to the particle energy and in-dependent of the type of radiation, except for veryheavy particles such as fission products. Proportionalcounters are also highly linear, but the proportionalityfactor for these is not entirely independent of the typeof radiation. Scintillation counters are linear fory-radiation, but not for a particles, for example, andthe type of radiation here also has some effect.

The resolution of semiconductor counters in the de-tection of {J- and y-radiation is largely determined by thenoise and is therefore to some extent independent ofthe energy. At an energy greater than about 0.5 MeVstatistical fluctuations in the ionization charge begin tobecome significant and the line width increases in pro-portion to ]IE. In proportional counters and scintilla-tion counters the resolution is primarily determined byfluctuations in the multiplication mechanism; thesefluctuations are also proportional to VË, but the pro-portionality factor is considerably greater.

By way of illustration to the foregoing,jig. 13 showsthe resolution, for X-rays and y-rays, of a semicon-ductor counter, a proportional counter and a scintilla-tion counter as functions of ]IE. In this figure the linewidth at half height is again used as a measure of theresolution. The resolution of the semiconductor coun-ters is seen to be better than that of the other two ex-cept for soft radiation, where the amplifier noise pre-dominates.

It may be recalled here that the average ionization energy IV

for germanium and silicon is only a few electron-volts (2.9 and3.6 eV respectively) and the Fano factor 0.1 to 0.15 as againstIV"" 30 eV and F*",,0.2 to 0.3 for gases. A direct comparison withthe scintillation counter is of course not possible, as this does notmeasure the ionization charge; it is however possible to char-acterize the relative spread in the output signals by fictitious valuesfor IV and F*. These are very high: 300 eV and 1 respectively.

In the detection of a-radiation with semiconductorcounters the resolution is partly determined by thefact that a relatively large number of recombinationstake place in the ionization track owing to the highcarrier densities involved; their number fluctuates,largely because of the inhomogeneous distribution of

the recombination centres. The resolution here is about20 keY. Although for a-radiation the resolution istherefore rather worse than for {J- or y-radiation, it isstill three times better than that of the detector previ-ously used for a spectroscopy, the ionization chamber.This advantage is due to the lower ionization energy,which results in a better signal-to-noise ratio.

Pulse rise-time

The rise time of the pulses obtained with semicon-ductor counters depends on the thickness of the sensit-ive layer, on the applied voltage and on the temperature,and lies between 10-8 and 10-5 s. Scintillation countersare in general somewhat faster: depending on the na-ture of the crystal and on the photomultiplier tube, risetimes in these counters are between 10-9 and 10-6 s.

2 3 4MeV

Fig. 13. Comparison of the X-ray and y-ray resolution of semi-conductor counters (curve 1), proportional counters (curve 2)and scintillation counters (curve 3). The half-height width of thepulse-height distribution obtained with a good counter for mono-chromatic radiation is plotted against the square root of thequantum energy E. Except for very small values of E, the semi-conductor counters are superior. The horizontal part of curve 1represents amplifier noise.

Proportional counters have a rise time of about 10-6 s;theyare therefore generally somewhat slower than semi-conductor counters. It should be remembered here thatthe rise time of a proportional counter is not a measureof the maximum count rate that can be handled;this is appreciably lower than would follow from therise time because, after very pulse, it takes some timebefore the generated ions have disappeared again.Ionization chambers are very much slower: these havea rise time of not less than about 10-3 s, owing to thelow mobility of positive and negative gas ions.

Other features

In solids the range of charge particles is much shorterthan in gases and the absorption of y-rays is muchgreater. These effects enable semiconductor counters tobe very much smaller than proportional counters and

[14] w. K. Hofker et al., IEEE Trans. nucl. Sci. NS-13, No. 3,208, 1966.

336 PHILIPS TECHNICAL REVIEW VOLUME27

yet still be useful for a wide range of energies. Completesemiconductor counters are even smaller than scintilla-tion counters, which have to be used in conjunctionwith a light-guide and photomultipliér tube.

The small dimensions of semiconductor counters area great advantage ~n various applications, such as inmedical and biological experiments. On the other hand,for measurements on very large specimens, or on spe-cimens that cannot be situated close to the detector,the small size is a disadvantage, because much of theemitted radiation is then no longer incident on thedetector. This disadvantage can usually be overcomeby using more than one detector, and placing themaround the specimen. It also appears likely that in thefuture it will be possible to make larger semiconductorcounters than at present.

Semiconductor detectors have the considerable prac-tical advantage of not requiring a well-stabilized vol-tage source. If they are connected, as shown in fig. 2,to an amplifier with capacitive negative feedback, theheight of the output pulses from the amplifier will belargely independent of the variations in the voltage Voacross the detector. The reason for this is that variationof Vo causes a change in the capacitance C of electrode2 with respect to earth such that the change in theheight of the pulses across R is exactly compensatedby the change in the ratio CICr ("charge amplifica-tion").

Finally, we should mention again that semiconductorcounters can be produced in a wide variety of forms.This makes it possible to adapt them more easily andmore effectively than other detectors to the require-ments of specific experiments.

It will be apparent from what we have said that semi-conductor detectors are preferable to other types forseveral types of measurement. Some examples havebeen specifically mentioned. In nuclear physics, theadvent of the semiconductor detector has broughtabout a considerable advance in spectroscopy and inparticle identification. We have also seen that the direc-tional distribution of radiation emitted as a result of anuclear reaction can be determined very much fasterwith a semiconductor counter, with no sacrifice ofaccuracy.

In radiochemistry also, which mainly requires thedetection of y-rays, semiconductor counters are oftento be preferred. This applies both for purely scientificresearch and for applied radiation chemistry such asactivation analysis. In such applications the very highenergy resolution of semiconductor counters often per-mits a simplification of procedures.

Summary. Germanium and silicon counters with P-N and P-I-Nconfigurations are extremely useful for detecting and measuringthe energy of y-quanta and high-energy charged particles. Ex-cept with very heavy particles these semiconductor detectors arehighly linear and have a particularly high resolution (about 20 keVfor a-radiation, only a fewkeV for fJ- and y-radiation). The pulseheight depends only on the quantum energy (particle energy)E and not on the nature of the radiation. With extremely thindetectors it is also possible to measure dE/dx and thus identifyunknown heavy particles. The construction ofthe device is readilyadaptable to specific requirements; to measure directional distri-butions, for example, a detector can be divided into numeroussub detectors (checker-board counter). The resolution is higher forlarger values of the charge carrier life compared with the transittime in thecounter, and for lower bias current. A P-I-N detectorcombines a large detection volume with a small bias current.